Reports from U.S. publications confirm that Gossip Girl actress Blake, 27, went into labour some time before New Year, which was a few weeks earlier than expected.
Despite this, both mum and baby are said to be doing well following the birth in Bedford, New York, though representatives of the couple are yet to officially respond to the media.
Blake previously spoke of her joy at becoming a mum, saying: 'I knew I wanted to have a lot of kids because I had come from a big family so it was always important to me.'
The star added she was 'excited' at the prospect of becoming a mother, two years after marrying Green Lantern star Reynolds.
Lively shared her exciting baby news on her lifestyle site, Preserve, earlier in 2014, though interestingly she has yet to confirm that her little one has arrived.
Ryan, who was previously married to bombshell Scarlett Johansson before marrying Blake, will no doubt be over the moon with the birth of his first child.
Congratulations to Ryan and Blake - who will surely have one of the most beautiful babies ever!